Answer:
Koffi's monthly salary: $3500 ($42000 annually)
Pete's monthly salary: $4416.7 ($53000 annually)
Pat's monthly salary: $8750 ($105000 annually)
Step-by-step explanation:
Let x represent Pat's annual salary
Let y represent Pete's annual salary
Let z represent Koffi's annual salary
According to the question, their annual salaries sum up to$200000 i.e. x + y + z= $200000
Pete makes $11000 more than Koffi anually means that y = $11000 + z
Pat makes $1000 less than twice (×2) of Pete's annual salary i.e. x = 2y - $1000
Hence, we have 3 equations:
(1)..... x + y + z= $200000
(2).... y = $11000 + z
(3).... x = 2y - $1000
First, we substitute y into equation (3) i.e.
x = 2(11000 + z) - 1000
x = 22000 + 2z - 1000
x = 21000 + 2z............ (4)
We then insert equations (4) and (2) into equation (1) to get z:
x + y + z = 200000
21000 + 2z + 11000 + z + z = 200000
4z + 32000 = 200000
4z = 200000 - 32000
4z = 168000
z = 42000
Hence, z (Koffi's) annual salary is $42000.
To get y, we substitute z in equation (2).
y = 11000 + z
y = 11000 + 42000
y = 53000
Hence, y (Pete's) annual salary is $53000
To get x, we add $42000 with $53000, and subtract from $200000 i.e. 42000 + 53000 = 95000
200000 - 95000 = 105000
Hence, x (Pat's) annual salary is $105000.
In order to get the monthly salary of each individual, we divide their annual salary by 12:
Koffi (z) = 42000/12 = $3500
Pete (y) = 53000/12 = $4416.7
Pat (x) = 105000/12 = $8750
= x.